Garrett M. Odell

The segment polarity network is a robust developmental module

All insects possess homologous segments, but segment specification differs radically among insect orders. In Drosophila, maternal morphogens control the patterned activation of gap genes, which encode transcriptional regulators that shape the patterned expression of pair-rule genes. This patterning cascade takes place before cellularization. Pair-rule gene products subsequently ‘imprint’ segment polarity genes with reiterated patterns, thus defining the primordial segments. This mechanism must be greatly modified in insect groups in which many segments emerge only after cellularization. In beetles and parasitic wasps, for instance, pair-rule homologues are expressed in patterns consistent with roles during segmentation, but these patterns emerge within cellular fields. In contrast, although in locusts pair-rule homologues may not control segmentation, some segment polarity genes and their interactions are conserved. Perhaps segmentation is modular, with each module autonomously expressing a characteristic intrinsic behaviour in response to transient stimuli. If so, evolution could rearrange inputs to modules without changing their intrinsic behaviours. Here we suggest, using computer simulations, that the Drosophila segment polarity genes constitute such a module, and that this module is resistant to variations in the kinetic constants that govern its behaviour.

Cellular motions and thermal fluctuations: the Brownian ratchet

We present here a model for how chemical reactions generate protrusive forces by rectifying Brownian motion. This sort of energy transduction drives a number of intracellular processes, including filopodial protrusion, propulsion of the bacterium Listeria, and protein translocation.

Robustness, Flexibility, and the Role of Lateral Inhibition in the Neurogenic Network

BACKGROUND Many gene networks used by developing organisms have been conserved over long periods of evolutionary time. Why is that? We showed previously that a model of the segment polarity network in Drosophila is robust to parameter variation and is likely to act as a semiautonomous patterning module. Is this true of other networks as well? RESULTS We present a model of the core neurogenic network in Drosophila. Our model exhibits at least three related pattern-resolving behaviors that the real neurogenic network accomplishes during embryogenesis in Drosophila. Furthermore, we find that it exhibits these behaviors across a wide range of parameter values, with most of its parameters able to vary more than an order of magnitude while it still successfully forms our test patterns. With a single set of parameters, different initial conditions (prepatterns) can select between different behaviors in the networks repertoire. We introduce two new measures for quantifying network robustness that mimic recombination and allelic divergence and use these to reveal the shape of the domain in the parameter space in which the model functions. We show that lateral inhibition yields robustness to changes in prepatterns and suggest a reconciliation of two divergent sets of experimental results. Finally, we show that, for this model, robustness confers functional flexibility. CONCLUSIONS The neurogenic network is robust to changes in parameter values, which gives it the flexibility to make new patterns. Our model also offers a possible resolution of a debate on the role of lateral inhibition in cell fate specification.

In silico reconstitution of Listeria propulsion exhibits nano-saltation.

To understand how the actin-polymerization-mediated movements in cells emerge from myriad individual protein–protein interactions, we developed a computational model of Listeria monocytogenes propulsion that explicitly simulates a large number of monomer-scale biochemical and mechanical interactions. The literature on actin networks and L. monocytogenes motility provides the foundation for a realistic mathematical/computer simulation, because most of the key rate constants governing actin network dynamics have been measured. We use a cluster of 80 Linux processors and our own suite of simulation and analysis software to characterize salient features of bacterial motion. Our “in silico reconstitution” produces qualitatively realistic bacterial motion with regard to speed and persistence of motion and actin tail morphology. The model also produces smaller scale emergent behavior; we demonstrate how the observed nano-saltatory motion of L. monocytogenes, in which runs punctuate pauses, can emerge from a cooperative binding and breaking of attachments between actin filaments and the bacterium. We describe our modeling methodology in detail, as it is likely to be useful for understanding any subcellular system in which the dynamics of many simple interactions lead to complex emergent behavior, e.g., lamellipodia and filopodia extension, cellular organization, and cytokinesis.

An agent-based model contrasts opposite effects of dynamic and stable microtubules on cleavage furrow positioning

From experiments by Foe and von Dassow (Foe, V.E., and G. von Dassow. 2008. J. Cell Biol. 183:457–470) and others, we infer a molecular mechanism for positioning the cleavage furrow during cytokinesis. Computer simulations reveal how this mechanism depends on quantitative motor-behavior details and explore how robustly this mechanism succeeds across a range of cell sizes. The mechanism involves the MKLP1 (kinesin-6) component of centralspindlin binding to and walking along microtubules to stimulate cortical contractility where the centralspindlin complex concentrates. The majority of astral microtubules are dynamically unstable. They bind most MKLP1 and suppress cortical Rho/myosin II activation because the tips of unstable microtubules usually depolymerize before MKLP1s reach the cortex. A subset of astral microtubules stabilizes during anaphase, becoming effective rails along which MKLP1 can actually reach the cortex. Because stabilized microtubules aim statistically at the equatorial spindle midplane, that is where centralspindlin accumulates to stimulate furrow formation.

The mechanochemistry of cytogels

Abstract We present a mechanochemical model for force generation by actomyosin cytogel. The model is built around the observation that calcium ions both solate actomyosin gels and stimulate active contraction of the gel. The model cytogel can mimic a variety of morphogenetic pattern-producing phenomena.

Necessary and sufficient conditions for chemotactic bands

Abstract Traveling band solutions of the differential equations for chemotactic bacteria are exhibited for arbitrary motility μ( s ), chemotactic sensitivity χ( s ), and substrate consumption rate k ( s ). The requirements that the total number of bacteria in the band be finite, and that these bands behave appropriately at ± ∞, impose stringent constraints on the functions μ, χ, and k . These constraints are exhibited, and constitute the necessary and sufficient conditions for the existence of travelling bands of chemotactic bacteria.

An Algorithm for Locating and Displaying the Intersection of Two Arbitrary Surfaces

A new method for numerically computing the intersection of implicitly defined surfaces provides the capability to display intersections that are impossible to find analytically.

An experimental and computational study of the effect of ActA polarity on the speed of Listeria monocytogenes actin-based motility.

Listeria monocytogenes is a pathogenic bacterium that moves within infected cells and spreads directly between cells by harnessing the cells dendritic actin machinery. This motility is dependent on expression of a single bacterial surface protein, ActA, a constitutively active Arp2,3 activator, and has been widely studied as a biochemical and biophysical model system for actin-based motility. Dendritic actin network dynamics are important for cell processes including eukaryotic cell motility, cytokinesis, and endocytosis. Here we experimentally altered the degree of ActA polarity on a population of bacteria and made use of an ActA-RFP fusion to determine the relationship between ActA distribution and speed of bacterial motion. We found a positive linear relationship for both ActA intensity and polarity with speed. We explored the underlying mechanisms of this dependence with two distinctly different quantitative models: a detailed agent-based model in which each actin filament and branched network is explicitly simulated, and a three-state continuum model that describes a simplified relationship between bacterial speed and barbed-end actin populations. In silico bacterial motility required a cooperative restraining mechanism to reconstitute our observed speed-polarity relationship, suggesting that kinetic friction between actin filaments and the bacterial surface, a restraining force previously neglected in motility models, is important in determining the effect of ActA polarity on bacterial motility. The continuum model was less restrictive, requiring only a filament number-dependent restraining mechanism to reproduce our experimental observations. However, seemingly rational assumptions in the continuum model, e.g. an average propulsive force per filament, were invalidated by further analysis with the agent-based model. We found that the average contribution to motility from side-interacting filaments was actually a function of the ActA distribution. This ActA-dependence would be difficult to intuit but emerges naturally from the nanoscale interactions in the agent-based representation.

A computer simulation of chemical signaling during the aggregation phase of Dictyostelium discoideum

Abstract A model for chemical signaling among cells during the aggregation phase of the cellular slime mold Dictyostelium discoideum is simulated using a computer. The resulting chemical concentration profiles are considered in terms of experimental observations. Considerable emphasis is placed on examination of the chemical environment at the center of an aggregation. Its unique nature suggests a mechanism for initially establishing the location of center. Effects of the dimensionality of the simulation universe are also discussed.